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Equation 2 · Part 7 · What a Biosignature Has to Rule Out

addition

P(L∣D)=P(D∣L) P(L)P(D∣L) P(L)+P(D∣L‾) P(L‾),P(L \mid D) = \frac{P(D \mid L)\, P(L)}{P(D \mid L)\, P(L) + P(D \mid \overline{L})\, P(\overline{L})},
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

The passage around this formula

The first is inferential. Catling and colleagues set out a Bayesian framework in which biogeochemical models of an Exo-Earth system simulate what would be observed with and without a biosphere, and observations are then scored against both. The posterior probability of life takes the standard form P(L∣D)=P(D∣L) P(L)P(D∣L) P(L)+P(D∣L‾) P(L‾)P(L \mid D) = \frac{P(D \mid L)\, P(L)}{P(D \mid L)\, P(L) + P(D \mid \overline{L})\, P(\overline{L})}. where D is the data and L the life hypothesis. The framework’s own emphasis is that confidence improves as abiotic false-positive scenarios become demonstrably implausible — that is, as the term P(D ∣\mid L‾\overline{L}) is driven down — at which point the prior matters less to the conclusion [ 3 ] . The structure makes the article’s thesis formal: the numerator is the…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.